Answer:
Step-by-step explanation:
B) Small triangle:
height = 20 - 15 = 5
base = 1
height to base = 5 :1
Medium triangle :
height = 60 -30 = 30
base = 2
height to base = 30 :2 = 15 :1
Large triangle:
height = 120 - 60 = 60
base = 4
height to base = 60 : 4 = 15 : 1
c) The ratios are same. This is true because wage and working hours are in direct proportion.
E) Take any two points. (1 , 15) & (2 , 30). Find the slope.
Slope = Change in y ÷ change in x
m = (30-15) ÷ (2 -1) = 15/1 = 15
y -y1 = m(x -x1)
y - 15 = 15(x - 1)
y - 15 = 15x - 15
y = 15x - 15 + 15
y = 15x
Solution :
Along the edge 
The parametric equation for
is given :

Along edge 
The curve here is a quarter circle with the radius 9. Therefore, the parametric equation with the domain
is then given by :


Along edge 
The parametric equation for
is :

Now,
x = 9t, ⇒ dx = 9 dt
y = 0, ⇒ dy = 0

And


Then :

![$=\int_0^1 \left[\left( 9 \sin \frac{\pi}{2}t\right)^2\left(9 \cos \frac{\pi}{2}t\right)\left(-\frac{7 \pi}{2} \sin \frac{\pi}{2}t dt\right) + \left( 9 \cos \frac{\pi}{2}t\right)^2\left(9 \sin \frac{\pi}{2}t\right)\left(\frac{7 \pi}{2} \cos \frac{\pi}{2}t dt\right) \right]$](https://tex.z-dn.net/?f=%24%3D%5Cint_0%5E1%20%5Cleft%5B%5Cleft%28%209%20%5Csin%20%5Cfrac%7B%5Cpi%7D%7B2%7Dt%5Cright%29%5E2%5Cleft%289%20%5Ccos%20%5Cfrac%7B%5Cpi%7D%7B2%7Dt%5Cright%29%5Cleft%28-%5Cfrac%7B7%20%5Cpi%7D%7B2%7D%20%5Csin%20%5Cfrac%7B%5Cpi%7D%7B2%7Dt%20dt%5Cright%29%20%2B%20%5Cleft%28%209%20%5Ccos%20%5Cfrac%7B%5Cpi%7D%7B2%7Dt%5Cright%29%5E2%5Cleft%289%20%5Csin%20%5Cfrac%7B%5Cpi%7D%7B2%7Dt%5Cright%29%5Cleft%28%5Cfrac%7B7%20%5Cpi%7D%7B2%7D%20%5Ccos%20%5Cfrac%7B%5Cpi%7D%7B2%7Dt%20dt%5Cright%29%20%5Cright%5D%24)
![$=\left[-9^4\ \frac{\cos^4\left(\frac{\pi}{2}t\right)}{\frac{\pi}{2}} -9^4\ \frac{\sin^4\left(\frac{\pi}{2}t\right)}{\frac{\pi}{2}} \right]_0^1$](https://tex.z-dn.net/?f=%24%3D%5Cleft%5B-9%5E4%5C%20%5Cfrac%7B%5Ccos%5E4%5Cleft%28%5Cfrac%7B%5Cpi%7D%7B2%7Dt%5Cright%29%7D%7B%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%20-9%5E4%5C%20%5Cfrac%7B%5Csin%5E4%5Cleft%28%5Cfrac%7B%5Cpi%7D%7B2%7Dt%5Cright%29%7D%7B%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%20%5Cright%5D_0%5E1%24)
= 0
And
x = 0, ⇒ dx = 0
y = 9 t, ⇒ dy = 9 dt

Therefore,

= 0 + 0 + 0
Applying the Green's theorem


Here,



Therefore,


The vector field F is =
is conservative.
Answer:
x>60 or x=60
Step-by-step explanation:
The must be 60 or more inches.
Answer:
8
Step-by-step explanation:
Answer:
a. 2 – 8 - [- 4 – (-6 + 3 -9)] X ( -10 ÷2) suprimir los signos de agrupacion
Step-by-step explanation: